I've not used a chainmail scrubber, so I don't have an opinion on them yet. I have good success with Lodge's polycarbonate scraper for any stuck bits, and a nylon brush as you recommend. Here's my cleanup process if you're interested.

I just had the opportunity to use this scrub brush a couple days ago and immediately ordered one. It does not have a scraper on the back like the IKEA one you linked to, or the brush I already have, but I use the Lodge scraper anyway, and it has nice sharp edges that have held up well for years. The thing I really like about the Scotch-Brite brush I linked to is the extra stiff thin rows of bristles on the back where a scraper would be. It works really well in tight corners like the lip around the edge of my Dutch oven covers.

Hello fellow drunk and now cast iron owner. Having used cast irons for a while now and converted my family to use them as well here are 2 things i recommend to all

Chain mail style cleaning device. It's basically all i use now: https://www.amazon.com/Ringer-Original-Stainless-Cleaner-Patented/dp/B00FKBR1ZG/ref=sr_1_5?keywords=cast+iron+cleaner&qid=1576123455&sr=8-5

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Whatever the fuck this thing is for basically scraping all the shit off: https://www.amazon.com/Lodge-Scrapers-Handheld-Polycarbonate-Cleaners/dp/B0039UU9UO/ref=sxin_3_ac_d_rm?ac_md=1-1-Y2FzdCBpcm9uIHNjcmFwZXI%3D-ac_d_rm&keywords=cast+iron+cleaner&pd_rd_i=B0039UU9UO&pd_rd_r=5f7d4e32-1848-4b66-8702-3c198848aa90&pd_rd_w=ojyzg&pd_rd_wg=o6TMn&pf_rd_p=6d29ef56-fc35-411a-8a8e-7114f01518f7&pf_rd_r=1GKAZRCA4W5AESNDMXGT&psc=1&qid=1576123574